Look i m not trying to diss you, just throw some constructive criticism (i used to make the exact same mistakes):
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I always end up just walking around the club looking at people dance.
As you walk around the club, instead of checking out hot girls dancing in a creepy way make eye contact with the girls sitting around and open them. If you get rejected it s no big deal, you were just walkin away anyways
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Last weekend I bought a girl some drinks and tried to dance with her
Never buy a girl drinks (or any gifts for that matter) until you got something from her. If you do she ll think you re desperate
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Once I know I have something deeply in common with a girl (i.e. we're in the same class, we're in the same clubs, we have a strong mutual friend) then I'm good to go
if by "good to go" you re referring to your progress towards LJBF-land, then you re right, you're almost there...

Remember, you wanna flirt with a girl and one of the best ways to do that is by remaining mysterious... hard to do when you tell her all about you and keep talking about your common interests.
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I always think, "She's going to think I'm weird for going up and talking to her".
this has been said thousands of times on this forum and other similar ones, but i ll repeat it one more time: girls WANT to be approached. Why do you think she put in all the effort to look good and get ready for the club? to sit there quietly wit her friends all night? girls want action, they want to be approached by fun guys, that s why they re there in teh first place! However also keep in mind that most girls have a "bitch shield" which they ll use automatically when you open them, you just have to get past it, don't let it discourage you.
good luck!